What decimal number does the bit pattern 01100101 represent

What decimal number does the bit pattern 01100101 represent if it is a sign-magnitude integer?

Solution

for a signed magnitude integer the value is \"positive\" if the left most bit is \"0\". and the value is \"negative\" if the left most bit is \"1\".

here the given bit pattern is 01100101 so the left most bit is \"0\" then we say the value is positive value.

decimal representation:

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bit pattern is --- 0 1 1 0 0 1 0 1

place values are 2⁷ 2⁶ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰

answer is 0*2⁷ + 1* 2⁶ + 1*2⁵ + 0*2⁴ + 0*2³ + 1*2² + 0*2¹ + 1* 2⁰

⁼ 2⁶ + 2⁵  + 2² + 2⁰

= 64 + 32 + 4 + 1

= 101

so the decimal representation of signed magnitude integer bit pattern is ( 01100101 )₂ = ( 101 )₁₀